A089355 A quarter-square shaped (A002620) staircase array distributing the frequency of objects counted by A047970.
1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 4, 2, 2, 1, 4, 3, 8, 7, 9, 5, 5, 1, 1, 5, 4, 13, 14, 23, 20, 25, 16, 14, 7, 2, 1, 1, 6, 5, 19, 23, 44, 49, 71, 65, 75, 60, 48, 32, 18, 6, 1, 1, 7, 6, 26, 34, 73, 94, 154, 172, 232, 234, 249, 228, 195, 145, 101, 59, 27, 9, 2
Offset: 1
Examples
The array begins: 1..1..1..1..1..1..1.... ...1..2..3..4..5..6.... ......1..2..3..4..5.... ......1..4..8.13.19.... where the fourth row counts the ordered partitions of type 221^k and type 41^k since (1 3 6 10 15 ...) + (0 1 2 3 4 ...) yields the required result.